is different from that on \(M_-\)  which has a similar form but with \(\omega _H\rightarrow -\omega _H\)  changing thus the sign of the last term due to the de Sitter gravity. Both these equations can be solved analytically. For example, in conformal frame the general solution may be written as a mode integral [1]},
\(\psi ({x}_c\,)= \int d^{3}p\sum _{\sigma }[U_{{\bf p},\sigma }(x_c){\alpha }({\bf p},\sigma )+V_{{\bf p},\sigma }(x_c){\beta }^{*}({\bf p},\sigma )]\,,\) 
